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Space - Mathematics and space | | Space - Mathematics and space: Encyclopedia II - Space - Mathematics and space | | In mathematics, a space is a set, with some particular properties and usually some additional structure. It is not a formally defined concept as such, but a generic name for a number of similar concepts, most of which generalize some abstract properties of the physical concept of space.
In particular, a vector space and specifically a Euclidean space can be seen as generalizations of the concept of a Euclidean coordinate system. Important varieties of vector spaces with more imposed structure include Banach space and Hilbert space. Distance measurement is abstracted as the concept of metric space and volume mea ...
See also:Space, Space - Physics and Space, Space - Measurement, Space - Astronomy and space, Space - Mathematics and space, Space - The philosophy of space, Space - The psychology of space, Space - Anxiety and space, Space - Personal space, Space - Use of space, Space - Reference | | | Space, Space - Anxiety and space, Space - Astronomy and space, Space - Mathematics and space, Space - Measurement, Space - Personal space, Space - Physics and Space, Space - Reference, Space - The philosophy of space, Space - The psychology of space, Space - Use of space, Outer space, Space exploration | | |
| | | Space: Encyclopedia II - Space - Mathematics and space
Space - Mathematics and space
In mathematics, a space is a set, with some particular properties and usually some additional structure. It is not a formally defined concept as such, but a generic name for a number of similar concepts, most of which generalize some abstract properties of the physical concept of space.
In particular, a vector space and specifically a Euclidean space can be seen as generalizations of the concept of a Euclidean coordinate system. Important varieties of vector spaces with more imposed structure include Banach space and Hilbert space. Distance measurement is abstracted as the concept of metric space and volume measurement leads to the concept of measure space.
As far as the concept of dimension is defined, this need not be 3: it can also be 0 (a point), 1 (a line), 2 (a plane), more than 3, and with some definitions, a non-integer value. Mathematicians often study general structures that hold regardless of the number of dimensions.
Kinds of mathematical spaces include:
- Banach space
- Euclidean space
- Hilbert space
- Metric space
- Probability space
- Projective space
- Topological space
- Vector space
Other related archivesAirspace, Astronomy, Banach space, Cartography, Critique of Pure Reason, Earth, Earth's atmosphere, Environments, Euclidean space, Geography, Geometry, Gottfried Leibniz, Henri Poincaré, Hilbert space, Immanuel Kant, International System of Units, Isaac Newton, Karman line, Metric space, Outer space, Probability space, Projective space, Public space, Relativistic physics, Space exploration, Spatial planning, Topological space, Topology, Vector space, a priori, abstract, agoraphobia, amodal perception, ancient Greeks, anxiety, architecture, astronomy, atmospheres, bucket argument, celestial body, classical physics, claustrophobia, conceptual, coordinates, dimension, dimensions, distance traveled by light in a vacuum, events, farming, framework, fundamental, hunting, manifold, mass, mathematics, measure space, measurement, measurements, meter, metric space, number, object permanence, objects, ontological, outer space, ownership, perception, philosophers, philosophical, physics, plasma, private property, property, psychology, quantify, science, scientists, self preservation, set, spacetime, sphere-world, structure, substances, time, universe, vector space, waters
 Adapted from the Wikipedia article "Mathematics and space", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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